This study extends previous work on modeling water sorption, dilation, and diffusion in polybenzimidazoles (PBIs) by comparing water transport properties of commercial PBI (Celazole®) with three sulfone-containing PBIs. A model is developed combining free volume and partial immobilization theories to describe water diffusion coefficients across a wide range of concentrations and degrees of swelling. Water vapor sorption and dilation follow dual-mode behavior and generally correlate with the availability of strong hydrogen bonding sites on the polymer chains. At low concentrations, water diffusion coefficients are suppressed by partial immobilization of Langmuir species, while at high concentrations, water diffusion coefficients increase due to significant swelling and plasticization. To account for the influence of plasticization on free volume and water mobility, local Henry's law mobility coefficients are correlated with fractional free volume (FFV), where the volume occupied by water molecules is considered to contribute to dynamic free volume and is assumed to be as accessible for water diffusion as unoccupied free volume. Contributions to diffusion coefficients from thermodynamic and convective frame of reference effects and concentration averaging are also considered.

这项研究通过比较商用PBI（Celazole®）与三种含砜的PBI的水传输特性，扩展了先前对聚苯并咪唑（PBI）中的吸水，扩散和扩散进行建模的工作。结合自由体积和部分固定理论开发了一个模型，用于描述水在各种浓度和溶胀度范围内的扩散系数。水蒸气的吸附和扩散遵循双模式行为，通常与聚合物链上强氢键位的可用性相关。在低浓度下，Langmuir物种的部分固定会抑制水扩散系数，而在高浓度下，由于明显的溶胀和增塑作用，水扩散系数会增加。为了考虑塑化对自由体积和水迁移率的影响，局部亨利定律迁移率系数与分数自由体积（FFV）相关，其中水分子占据的体积被认为有助于动态自由体积，并假定为可作为无人使用的自由体积进行水扩散。还考虑了参考效应和浓度平均的热力学和对流框架对扩散系数的贡献。